${\mathbb{Z}}_2$-graded identities of the Grassmann algebra over a finite field

Abstract

Let $F$ be a finite field with characteristic $p>2$ and let $G$ be the unitary Grassmann algebra generated by an infinite dimensional vector space $V$ over $F$. In this paper, we determine a basis of the ${\mathbb{Z}}_2$-graded polynomial identities for any non-trivial ${\mathbb{Z}}_2$-grading such that a basis of $V$ is homogeneous in this grading.

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